Visiting Turkey, Russia's Foreign Minister Sergey Lavrov demanded that barriers be removed to Russian food and fertiliser exports.
There are no western sanctions on these, but Mr Lavrov said obstacles “related to financing, logistics, transportation and insurance of Russian exports have remained and even have grown tougher”.
“If there is no further progress in removing barriers … we will think about whether this deal is necessary,” he told a press conference in Ankara, alongside his Turkish counterpart Mevlut Cavusoglu.
The grain deal was brokered by the UN and Turkey last year amid rising prices and fears for global food security.
It allowed for the re-opening of blockaded Black Sea ports, with Russia allowed to inspect cargoes.
Ukraine's ports can handle more grain than land routes, which are fraught with complications.
However, Moscow has complained that its own agricultural exports are considered too hot to handle because of sanctions on its banks and ships.
If Russia's demands are not met, “well, let them continue to ship the relevant products from Ukraine by land, by rail and by rivers”, said Mr Lavrov, who later met Turkish President Recep Tayyip Erdogan.
“And we will work, if necessary, outside the framework of this initiative,” said Mr Lavrov.
“We have the opportunity to do this.”
Russia agreed a short 60-day extension in March, in what Mr Lavrov described as a “small escalatory move” after the deal had previously operated for 120 days at a time.
“After we extended the deal for 120 days, we saw no indication that those issues could be solved and grew tired of appealing to the conscience of those who determine it,” Mr Lavrov said.
Ukraine is a top exporter of wheat, corn and sunflower oil.
The agreement has so far allowed the export of more than 25 million tonnes of grain and other agricultural products.
Mr Cavusoglu said Turkey “values the continuation of the agreement which is also important in terms of reducing the global food crisis”.